deletions | additions       diff --git a/subsubsection_sparsity_problem_However_with__.tex b/subsubsection_sparsity_problem_However_with__.tex  index 67e4b0e..fa3c4cd 100644  --- a/subsubsection_sparsity_problem_However_with__.tex  +++ b/subsubsection_sparsity_problem_However_with__.tex 
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\[ M_{K} = \left( \begin{array}{ccc}  0.0625 & 0.125 & 0.0625 \\  0.125 & 0.25 & 0.125 \\  0.0625 & 0.125 & 0.0625 \end{array} \right).\] \right)\]  Whereas the simple histogram method places a spike function (i.e. $K = \delta$) at the bin corresponding to $(x,y)$ and update only a single bin, Parzen windowing places a kernel at the bin of $(x,y)$ and updates all bins falling under the kernel with the corresponding kernel value.  As a result using a gaussian filter, the estimated distributions are more smooth and less sparse.